TSTP Solution File: GRP613-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP613-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:56:37 EDT 2022
% Result : Unsatisfiable 8.74s 8.88s
% Output : Proof 8.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP613-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : moca.sh %s
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jun 13 09:02:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 8.74/8.88 % SZS status Unsatisfiable
% 8.74/8.88 % SZS output start Proof
% 8.74/8.88 The input problem is unsatisfiable because
% 8.74/8.88
% 8.74/8.88 [1] the following set of Horn clauses is unsatisfiable:
% 8.74/8.88
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(A, inverse(B))), C)), double_divide(A, C)) = B
% 8.74/8.88 multiply(A, B) = inverse(double_divide(B, A))
% 8.74/8.88 multiply(inverse(a1), a1) = multiply(inverse(b1), b1) ==> \bottom
% 8.74/8.88
% 8.74/8.88 This holds because
% 8.74/8.88
% 8.74/8.88 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 8.74/8.88
% 8.74/8.88 E:
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(A, inverse(B))), C)), double_divide(A, C)) = B
% 8.74/8.88 f1(multiply(inverse(a1), a1)) = true__
% 8.74/8.88 f1(multiply(inverse(b1), b1)) = false__
% 8.74/8.88 multiply(A, B) = inverse(double_divide(B, A))
% 8.74/8.88 G:
% 8.74/8.88 true__ = false__
% 8.74/8.88
% 8.74/8.88 This holds because
% 8.74/8.88
% 8.74/8.88 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 8.74/8.88
% 8.74/8.88 double_divide(X0, double_divide(inverse(Y1), Y1)) = inverse(X0)
% 8.74/8.88 double_divide(X0, inverse(X0)) = double_divide(Y1, inverse(Y1))
% 8.74/8.88 double_divide(X0, inverse(X0)) = double_divide(inverse(Y1), Y1)
% 8.74/8.88 double_divide(Y0, double_divide(X0, inverse(X0))) = inverse(Y0)
% 8.74/8.88 double_divide(inverse(Y0), X1) = double_divide(inverse(inverse(X1)), inverse(Y0))
% 8.74/8.88 double_divide(inverse(Y0), Y0) = double_divide(inverse(X1), X1)
% 8.74/8.88 double_divide(inverse(double_divide(X0, inverse(X0))), Y1) = inverse(Y1)
% 8.74/8.88 double_divide(inverse(double_divide(inverse(X0), X0)), X1) = inverse(X1)
% 8.74/8.88 double_divide(X0, double_divide(X0, Y1)) -> Y1
% 8.74/8.88 double_divide(double_divide(Y0, double_divide(X1, inverse(X1))), double_divide(false__, inverse(false__))) -> Y0
% 8.74/8.88 double_divide(double_divide(Y0, double_divide(inverse(X1), X1)), double_divide(false__, inverse(false__))) -> Y0
% 8.74/8.88 double_divide(inverse(X1), double_divide(Y0, double_divide(inverse(inverse(X1)), inverse(double_divide(Y0, inverse(Y1)))))) -> Y1
% 8.74/8.88 double_divide(inverse(X1), double_divide(inverse(double_divide(X0, inverse(X1))), double_divide(X0, inverse(Y1)))) -> Y1
% 8.74/8.88 double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(inverse(Y2)), inverse(double_divide(inverse(Y1), inverse(X1))))), Y1)) -> Y2
% 8.74/8.88 double_divide(inverse(X1), double_divide(inverse(inverse(Y1)), inverse(X1))) -> Y1
% 8.74/8.88 double_divide(inverse(X2), double_divide(Y0, double_divide(inverse(double_divide(X1, inverse(double_divide(Y0, inverse(Y1))))), double_divide(X1, inverse(X2))))) -> Y1
% 8.74/8.88 double_divide(inverse(X3), double_divide(Y0, double_divide(X1, double_divide(inverse(double_divide(X2, inverse(double_divide(X1, inverse(X3))))), double_divide(X2, inverse(double_divide(Y0, inverse(Y1)))))))) -> Y1
% 8.74/8.88 double_divide(inverse(X4), double_divide(Y0, double_divide(X1, double_divide(X2, double_divide(inverse(double_divide(X3, inverse(double_divide(X2, inverse(double_divide(Y0, inverse(Y1))))))), double_divide(X3, inverse(double_divide(X1, inverse(X4))))))))) -> Y1
% 8.74/8.88 double_divide(inverse(Y0), double_divide(X0, inverse(X0))) -> Y0
% 8.74/8.88 double_divide(inverse(Y0), double_divide(Y1, double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(inverse(double_divide(Y1, inverse(Y3)))), inverse(X1))), inverse(Y0))))) -> Y3
% 8.74/8.88 double_divide(inverse(Y0), double_divide(Y1, double_divide(inverse(X3), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(double_divide(Y1, inverse(Y3)))))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y0))))) -> Y3
% 8.74/8.88 double_divide(inverse(Y0), double_divide(Y1, double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y0)))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(double_divide(Y1, inverse(Y3))))), X3))) -> Y3
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(inverse(double_divide(X2, inverse(X0))), double_divide(X2, inverse(inverse(Y0)))))), inverse(Y2)))) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(X1), double_divide(inverse(double_divide(inverse(inverse(Y0)), inverse(X1))), inverse(Y2)))) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(X3), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y0)))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y2)))) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(Y0), Y2)) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(X0), X0)), double_divide(inverse(inverse(Y0)), inverse(Y2)))) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(inverse(double_divide(X2, inverse(X0))), double_divide(X2, inverse(inverse(Y2)))))), inverse(Y0))), X1)) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y3)))), X2)), inverse(X3))), double_divide(X0, X2))), double_divide(inverse(double_divide(Y2, inverse(X3))), double_divide(Y2, inverse(Y0))))) -> Y3
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y2)))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y0))), X3)) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(double_divide(inverse(inverse(Y2)), inverse(X1))), inverse(Y0))), X1)) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), double_divide(inverse(double_divide(inverse(inverse(Y2)), inverse(X1))), double_divide(inverse(inverse(Y0)), inverse(X1)))) -> Y2
% 8.74/8.88 double_divide(inverse(Y0), inverse(double_divide(inverse(X1), X1))) -> Y0
% 8.74/8.88 double_divide(inverse(Y1), double_divide(Y0, double_divide(Y0, double_divide(inverse(X2), X2)))) -> Y1
% 8.74/8.88 double_divide(inverse(Y1), double_divide(inverse(Y2), Y2)) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(X0, inverse(Y1))), inverse(X0)) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(Y0, inverse(Y1))), double_divide(Y0, double_divide(inverse(X1), X1))) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(X1), X1)), inverse(Y1)) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(X1), Y2)), double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(X1))), double_divide(inverse(double_divide(X2, inverse(X0))), double_divide(X2, inverse(inverse(Y1)))))), Y2)) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(X1), Y2)), double_divide(inverse(double_divide(inverse(inverse(Y1)), inverse(X1))), Y2)) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(X3), Y2)), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y1)))), X2)), inverse(X3))), double_divide(X0, X2))), Y2)) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(Y1), Y2)), double_divide(inverse(double_divide(inverse(X0), X0)), Y2)) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(Y1), inverse(X1))), X1) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(Y1), inverse(Y3))), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(A, inverse(B))), C)), double_divide(A, C)) -> B
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(inverse(double_divide(X1, inverse(X0))), double_divide(X1, inverse(X2))))), X2) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(inverse(inverse(X1)), inverse(X0)))), X1) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X2), inverse(Y3))), double_divide(Y0, double_divide(inverse(double_divide(X1, inverse(double_divide(Y0, inverse(Y1))))), double_divide(X1, inverse(X2)))))), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(X3), inverse(Y3))), double_divide(Y0, double_divide(X1, double_divide(inverse(double_divide(X2, inverse(double_divide(X1, inverse(X3))))), double_divide(X2, inverse(double_divide(Y0, inverse(Y1))))))))), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(Y0), inverse(double_divide(inverse(X1), X1)))), inverse(Y2))), Y0) -> Y2
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X1), X1)), inverse(Y1))), inverse(Y2))), Y1) -> Y2
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X3), Y2)), inverse(Y3))), double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(inverse(Y1)))), X2)), inverse(X3))), double_divide(X0, X2))), Y2))), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(Y2), inverse(X1))), inverse(Y1))), Y2)), X1) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(X1))), X2)), inverse(Y1))), double_divide(X0, X2))), X1) -> Y1
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(X1, double_divide(inverse(double_divide(X2, inverse(double_divide(X1, inverse(X3))))), double_divide(X2, inverse(X0)))))), inverse(Y3))), X3)), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(X0), inverse(Y1))), double_divide(inverse(double_divide(X1, inverse(X0))), double_divide(X1, inverse(X2))))), inverse(Y3))), X2)), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(X1))), X2)), inverse(Y1))), double_divide(X0, X2))), inverse(Y3))), X1)), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X0, inverse(Y2))), X2)), inverse(X3))), double_divide(X0, X2))), inverse(Y1))), Y2)), inverse(Y3))), X3)), Y1) -> Y3
% 8.74/8.88 double_divide(inverse(double_divide(inverse(false__), false__)), double_divide(inverse(double_divide(inverse(X1), X1)), Y0)) -> Y0
% 8.74/8.88 double_divide(inverse(inverse(X0)), double_divide(inverse(X1), X0)) -> inverse(X1)
% 8.74/8.88 double_divide(inverse(inverse(Y1)), inverse(double_divide(inverse(Y1), inverse(X1)))) -> X1
% 8.74/8.88 double_divide(inverse(inverse(double_divide(inverse(X1), X1))), inverse(Y0)) -> Y0
% 8.74/8.88 f1(double_divide(X1, inverse(X1))) -> false__
% 8.74/8.88 f1(double_divide(X1, inverse(X1))) -> true__
% 8.74/8.88 f1(double_divide(double_divide(double_divide(false__, inverse(false__)), double_divide(false__, inverse(false__))), double_divide(X1, inverse(X1)))) -> false__
% 8.74/8.88 f1(double_divide(double_divide(inverse(X1), X1), double_divide(false__, inverse(false__)))) -> false__
% 8.74/8.88 f1(double_divide(double_divide(inverse(X1), X1), double_divide(false__, inverse(false__)))) -> true__
% 8.74/8.88 f1(double_divide(false__, inverse(false__))) -> false__
% 8.74/8.88 f1(double_divide(false__, inverse(false__))) -> true__
% 8.74/8.88 f1(double_divide(inverse(X1), X1)) -> false__
% 8.74/8.88 f1(double_divide(inverse(X1), X1)) -> true__
% 8.74/8.88 f1(inverse(double_divide(a1, inverse(a1)))) -> true__
% 8.74/8.88 f1(inverse(double_divide(b1, inverse(b1)))) -> false__
% 8.74/8.88 f1(multiply(inverse(a1), a1)) -> true__
% 8.74/8.88 f1(multiply(inverse(b1), b1)) -> false__
% 8.74/8.88 inverse(inverse(Y1)) -> Y1
% 8.74/8.88 multiply(A, B) -> inverse(double_divide(B, A))
% 8.74/8.88 true__ -> false__
% 8.74/8.88 with the LPO induced by
% 8.74/8.88 a1 > b1 > f1 > multiply > inverse > double_divide > true__ > false__
% 8.74/8.88
% 8.74/8.88 % SZS output end Proof
% 8.74/8.88
%------------------------------------------------------------------------------